Method and apparatus for correcting errors in a multiple subcarriers communication system using multiple antennas

ABSTRACT

A method for correcting errors in a multiple antenna system based on a plurality of sub-carriers and a transmitting/receiving apparatus supporting the same are disclosed. The method includes determining a phase shift based precoding matrix phase shifted at a predetermined phase angle, initially transmitting each sub-carrier symbol to a receiver in a packet unit by using the phase shift based precoding matrix, reconstructing the phase shift based precoding matrix to reduce a spatial multiplexing rate if a negative reception acknowledgement (NACK) is received from the receiver, and retransmitting the initially transmitted sub-carrier symbol by using the reconstructed phase shift based precoding matrix or by changing the phase shift based precoding matrix using offset information fed back from the receiver or random offset information.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.14/141,308, filed on Dec. 26, 2013, now U.S. Pat. No. 9,106,291,which isa continuation of U.S. application Ser. No. 13/652,406, filed on Oct.15,2012, now U.S. Pat. No. 8,645,782, which is a continuation of U.S.application Ser. No. 12/307,322, filed on Jul. 10, 2009, now U.S. Pat.No. 8,312,335, which is the National Stage filing under 35 U.S.C. §371of International Application No. PCT/KR2007/003295filed on Jul. 6, 2007,which claims the benefit of earlier filing date and right of priority toKorean Application No. 10-2006-0091278, filed on Sep. 20, 2006, and alsoclaims the benefit of U.S. Provisional Application No. 60/806,696, filedon Jul. 6, 2006, the contents of which are all hereby incorporated byreference herein in their entirety.

TECHNICAL FIELD

The present invention relates to a method for correcting errors in amultiple antenna system based on a plurality of sub-carriers to performan automatic repeat request scheme, and a transmitting and receivingapparatus supporting the same.

BACKGROUND ART

Recently, as information communication services have been popularized, avariety of multimedia services has appeared, and high-quality serviceshave appeared, a demand for a wireless communication service is rapidlyincreasing. In order to actively cope with such a tendency, it isnecessary to increase capacity of a communication system and improvereliability in data transmission. A method of increasing communicationcapacity in a wireless communication environment may include a method offinding a new available frequency band and a method of increasing theefficiency of a restricted resource. As the latter method,multiple-antenna transmission/reception technologies of mounting aplurality of antennas in a transceiver to additionally ensure a spacefor using a resource, thereby obtaining a diversity gain or transmittingdata via each of the antennas in parallel to increase transmissioncapacity are attracting much attention and are being actively developed.

Among the multiple-antenna transmission/reception technologies, ageneral structure of a multiple-input multiple-output (MIMO) systembased on an orthogonal frequency division multiplexing (OFDM) will nowbe described with reference to FIG. 1.

In a transmitter, a channel encoder 101 adds redundant bits totransmission data bits to reduce influence due to a channel or noise, amapper 103 converts data bit information into data symbol information, aserial-to-parallel converter 105 converts data symbols into paralleldata symbols to be carried in a plurality of sub-carriers, and amultiple-antenna encoder 107 converts the parallel data symbols intospace-time signals. A multiple-antenna decoder 109, a parallel-to-serialconverter 111, a demapper 113, and a channel decoder 115, which areincluded in a receiver, perform the inverse functions of themultiple-antenna encoder 107, the serial/parallel converter 105, themapper 103, and the channel encoder 101, respectively.

In a multiple-antenna OFMD system, a variety of technologies ofincreasing reliability in data transmission are required. Examples ofthe technologies include space-time code (STC), cyclic delay diversity(CDD), antenna selection (AS), antenna hopping (AH), spatialmultiplexing (SM), beamforming (BF), and precoding. Hereinafter, maintechnologies will be described in more detail.

The STC is a scheme for obtaining the spatial diversity gain bysuccessively transmitting same signals through different antennas in amultiple antenna environment. The following determinant represents abasic time-space symbol used in a system having two transmittingantennas.

$\frac{1}{\sqrt{2}}\begin{pmatrix}S_{1} & {- S_{2}^{*}} \\S_{2} & S_{1}\end{pmatrix}$

In the above determinant, row represents antennas and column representstime slots.

The cyclic delay diversity (CDD) is to obtain a frequency diversity gainat a receiver by allowing all antennas to transmit OFDM signals atdifferent delay values or different sizes when a system having aplurality of transmitting antennas transmits the OFDM signals. FIG. 2illustrates a transmitter of a multiple antenna system which uses acyclic delay diversity (CDD) scheme.

After the OFDM symbols are separately transmitted to each of theantennas through a serial-to-parallel converter and a multiple antennaencoder, they are added with a cyclic prefix (CP) for preventinginterchannel interference and then transmitted to the receiver. At thistime, a data sequence transmitted to the first antenna is transmitted tothe receiver as it is but a data sequence transmitted to the nextantenna is cyclic-delayed by a certain bit and then transmitted to thereceiver.

Meanwhile, if the aforementioned cyclic delay diversity scheme isimplemented in a frequency domain, the cyclic delay can be expressed bythe product of phase sequences. In other words, as shown in FIG. 3, datasequences in the frequency domain are multiplied by predetermineddifferent phase sequences (phase sequence 1 to phase sequence M) whichare differently set according to the antennas, and are subjected to aninverse fast Fourier transform (IFFT), thereby being transmitted to thereceiver. This is called a phase shift diversity scheme.

According to the phase shift diversity scheme, a flat fading channel canbe changed to a frequency selective channel, and frequency diversitygain or frequency scheduling gain can be obtained through channelcoding. In other words, as shown in FIG. 4, if a phase sequence isgenerated using cyclic delay of a great value in the phase shiftdiversity scheme, since a frequency selective period becomes short,frequency selectivity becomes high, and after all, the frequencydiversity gain can be obtained through channel coding. This is mainlyused in an open loop system.

Also, if a phase sequence is generated using cyclic delay of a smallvalue in the phase shift diversity scheme, since a frequency selectiveperiod becomes long, a closed loop system allocates a resource to themost excellent channel area to obtain a frequency scheduling gain. Inother words, as shown in FIG. 4, if a phase sequence is generated usingcyclic delay of a small value in the phase shift diversity scheme, acertain sub-carrier area of a flat fading channel has a great channelsize and other sub-carrier areas have a small channel size. In thiscase, if an orthogonal frequency division multiple access (OFDMA) systemwhich allows a plurality of users transmits a signal through sub-carrierhaving a great channel size for each user, a signal to noise ratio (SNR)may increase.

Meanwhile, the precoding scheme includes a codebook based precodingscheme which is used when feedback information is finite in a closedloop system and a scheme for quantizing and feeding back channelinformation. In the codebook based precoding scheme, an index of aprecoding matrix which is previously known to a transmitter/receiver isfed back to the transmitter to obtain SNR gain.

FIG. 5 illustrates the configuration of a transmitter/receiver of amultiple antenna system which uses the codebook based precoding scheme.The transmitter and the receiver have finite precoding matrixes P₁ toP_(L). The receiver feeds back an optimal precoding matrix index l tothe transmitter by using channel information, and the transmitterapplies a precoding matrix corresponding to the fed-back index totransmission data X₁ to X_(Mt). Table 1 illustrates an example of thecodebook which is applicable when 3-bit feedback information is used inan IEEE 802.16e system which supports a spatial multiplexing rate of 2and has two transmission antennas.

TABLE 1 Matrix index (binary) Column 1 Column2 000 1    0    0    1   001 0.7940 −0.5801 − j0.1818 −0.5801 + j0.1818 −0.7940 010 0.7940 0.0576 − j0.6051  0.0576 + j0.6051 −0.7940 011 0.7941 −0.2978 + j0.5298−0.2978 − j0.5298 −0.7941 100 0.7941  0.6038 − j0.0689  0.6038 + j0.0689−0.7941 101 0.3289  0.6614 − j0.6740  0.6614 + j0.6740 −0.3289 1100.5112  0.4754 + j0.7160  0.4754 − j0.7160 −0.5112 111 0.3289 −0.8779 +j0.3481 −0.8779 − j0.3481 −0.3289

Meanwhile, examples of improving reliability in data transmission in awireless communication environment include an Automatic Repeat reQuest(ARQ) scheme and a hybrid ARQ (HARQ) scheme. These schemes will now bedescribed in detail.

An orthogonal frequency division multiplexing (OFDM) system and itssimilar system define resource blocks defined in a time-frequency domainand use the resource blocks as a single unit. In a downlink, a basestation allocates at least one resource block to a specific userequipment in accordance with a given scheduling rule and transmits datathrough a corresponding resource block. Also, in an uplink, if the basestation selects a specific user equipment in accordance with a givenscheduling rule and allocates a resource block to the corresponding userequipment, the corresponding user equipment transmits data to the basestation through the allocated resource block. At this time, if frameloss or damage occurs in the data transmitted to the downlink or theuplink, the ARQ or the HARQ is used to correct corresponding errors.

Examples of the HARQ scheme include channel-adaptiveHARQ/channel-non-adaptive HARQ and chase combining scheme/incrementalredundancy scheme. In the channel-non-adaptive HARQ, frame modulation orthe number of available resource blocks for retransmission is performedas it is determined during initial transmission. The channel-adaptiveHARQ varies the above parameters depending on the current channelstatus. For example, according to the channel-non-adaptive HARQ, if atransmitting side transmits data by using eight resource blocks in caseof initial transmission, the transmitting side retransmits the data byusing eight resource blocks even in case of retransmission. According tothe channel-adaptive HARQ, even though the transmitting side transmitsdata by using eight resource blocks in case of initial transmission, thetransmitting side retransmits the data by using resource blocks morethan or less than eight resource blocks depending on the channel status.

Furthermore, the HARQ scheme can be classified into a chase combiningscheme and an incremental redundancy scheme depending on which packet istransmitted during retransmission. According to the chase combiningscheme, as shown in FIG. 6, the transmitting side retransmits a packethaving the same format as that used for initial transmission or samedata symbols in different formats during second or third transmission iferrors occur in the packet used for the initial transmission. The HARQscheme is similar to the ARQ scheme in that the receiving side transmitsNCK message to the transmitting side if the receiving side cannotdemodulate a packet. However, the HARQ scheme is different from the ARQscheme in that the receiving side stores a frame which is previouslyreceived in a buffer for a certain time period and if a correspondingframe is retransmitted, combines the retransmitted frame with thepreviously received frame to improve a receiving success rate. Theincremental redundancy scheme is different from the chase combiningscheme in that a packet having a format different from that of thepacket used for initial transmission can be retransmitted. In otherwords, as shown in FIG. 7, additional parity part of a channel code isonly retransmitted during the second or third retransmission to reduce achannel coding rate, thereby correcting packet errors.

In addition, the HARQ scheme can be classified into synchronous HARQ andasynchronous HARQ depending on whether retransmission performed aftertransmission failure of initial data is performed in accordance with agiven timing.

Since the aforementioned multiple antenna related scheme and the ARQrelated schemes have been developed independently, synergy effectaccording to combination of the schemes have not been obtained. In thisregard, a time-space symbol based HARQ has been suggested. Thetime-space symbol based HARQ is used in a multiple antenna system.According to the time-space symbol based HARQ, as shown in FIG. 8, adata transmission rate increases through a bell labs layered space time(BLAST) scheme during initial transmission, and if errors occur insymbols S1 and S2 of a specific time slot, a time-space symbol isapplied to the symbols of the corresponding time slot and thenretransmission is performed to improve transmission reliability.

However, the aforementioned time-space symbol based HARQ has severalproblems. First, the time-space symbol based HARQ has limitation in thatit is based on a flat fading channel whose change speed is relativelyslow. Second, if multiple codewords are used, it is inefficient in thatretransmission of all codewords is required even though errors occuronly in some of the codewords. Third, flexibility is deteriorated inthat initial transmission should be performed by a spatial multiplexingscheme such as BLAST. Finally, since the adaptive ARQ such asincremental redundancy cannot be used for the time-space based HARQ,efficient error correction cannot be performed.

DISCLOSURE OF THE INVENTION

Accordingly, the present invention is directed to a method forcorrecting errors in a multiple antenna system based on a plurality ofsub-carriers and a transmitting/receiving apparatus supporting the same,which substantially obviate one or more problems due to limitations anddisadvantages of the related art.

An object of the present invention is to provide a method for correctingerrors in a multiple antenna system based on a plurality of sub-carriersand a transmitting/receiving apparatus supporting the same, in which amultiple antenna related scheme is combined with an automatic repeatrequest scheme to simultaneously improve speed and reliability in datatransmission.

To achieve these objects and other advantages and in accordance with thepurpose of the invention, as embodied and broadly described herein, amethod for correcting errors in a multiple antenna system based on aplurality of sub-carriers includes determining a phase shift basedprecoding matrix phase shifted at a predetermined phase angle, initiallytransmitting each sub-carrier symbol to a receiver in a packet unit byusing the phase shift based precoding matrix, reconstructing the phaseshift based precoding matrix to reduce a spatial multiplexing rate if anegative reception acknowledgement (NACK) is received from the receiver,and retransmitting the initially transmitted sub-carrier symbol by usingthe reconstructed phase shift based precoding matrix. The method mayfurther include applying offset information fed back from the receiverto the precoding matrix.

In another aspect of the present invention, a transmitting and receivingapparatus which supports a method for correcting errors in a multipleantenna system based on a plurality of sub-carriers includes a precodingmatrix determination module determining a precoding matrix phase shiftedat a predetermined phase angle, a precoding matrix reconstruction modulethe precoding matrix to reduce a spatial multiplexing rate if a negativereception acknowledgement (NACK) is received from a receiver, and aprecoding module precoding each sub-carrier symbol through the precodingmatrix. The transmitting and receiving apparatus may further include anoffset application module applying offset information fed back from thereceiver to the precoding matrix.

In the above aspects, the number of columns corresponding to the reducedspatial multiplexing rate is selected from the determined phase shiftbased precoding matrix so that the precoding matrix is reconstructed toconsist of the selected columns only.

Furthermore, if errors occur only in some of the initially transmittedpackets, the retransmitting step includes retransmitting some packetswhere errors occur but does not transmit a new packet untilretransmission is completed. Also, the retransmitting step may includeretransmitting some packets where errors occur and transmit a newpacket. In both cases, the retransmitting step is performed throughantennas other than those through which the packets where errors occurare transmitted. Also, the retransmitting step may include selectingantennas having excellent channel status.

Furthermore, the initial transmitting step includes transmittingdifferent sub-carrier symbols to each antenna, and if errors occur inall of the initially transmitted packets, the retransmitting step isperformed to allow sub-carrier symbols of each antenna to haveorthogonality.

In still another aspect of the present invention, a method forcorrecting errors in a multiple antenna system based on a plurality ofsub-carriers includes determining a phase shift based precoding matrixphase shifted at a predetermined phase angle, initially transmittingeach sub-carrier symbol to a receiver in a packet unit by using thephase shift based precoding matrix, applying predetermined offsetinformation to the precoding matrix if a negative receptionacknowledgement (NACK) is received from the receiver, and retransmittingthe initially transmitted sub-carrier symbol by using the phase shiftbased precoding matrix to which the offset information has been applied.

In further still another aspect of the present invention, a transmittingand receiving apparatus which supports a method for correcting errors ina multiple antenna system based on a plurality of sub-carriers includesa precoding matrix determination module determining a precoding matrixphase shifted at a predetermined phase angle, an offset applicationmodule applying offset information fed back from the receiver to theprecoding matrix, and a precoding module precoding each sub-carriersymbol through the precoding matrix.

The offset information includes at least one of sub-carrier index offsetinformation and phase value offset information, or both of them. Also,the offset information is sub-carrier index offset information appliedto all sub-carriers, and the sub-carrier offset information is a fixedvalue.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram illustrating an orthogonal frequency divisionmultiplexing system having multiple transmitting/receiving antennas;

FIG. 2 is a schematic view illustrating a transmitter of a multipleantenna system based on a related art cyclic delay diversity scheme;

FIG. 3 is a schematic view illustrating a transmitter of a multipleantenna system based on a related art phase shift diversity scheme;

FIG. 4 illustrates graphs of two examples of a related art phase shiftdiversity scheme;

FIG. 5 is a schematic view illustrating a transmitter/receiver of amultiple antenna system based on a related art precoding scheme;

FIG. 6 illustrates a concept of a chase combining scheme of HARQ;

FIG. 7 illustrates a concept of an incremental redundancy scheme ofHARQ;

FIG. 8 illustrates a concept of a time-space symbol based HARQ scheme;

FIG. 9 illustrates a procedure of performing a related art phase shiftdiversity scheme in a system having four antennas and a spatialmultiplexing rate of 2;

FIG. 10 illustrates a procedure of performing a phase shift basedprecoding scheme according to the present invention in the system ofFIG. 9;

FIG. 11 is a precoding matrix used for a phase shift based precodingscheme according to the present invention in the system of FIG. 10;

FIG. 12 illustrates precoding matrixes for initial transmission andretransmission used if errors occur in all of a plurality of packetswhich are simultaneously transmitted in a multiple codeword (MCW)structure;

FIG. 13 illustrates precoding matrixes used in one embodiment of a phaseshift diversity ARQ scheme for the case where errors occur in some of aplurality of packets which are simultaneously transmitted in an MCWstructure;

FIG. 14 illustrates precoding matrixes used in another embodiment of aphase shift diversity ARQ scheme for the case where errors occur in someof a plurality of packets which are simultaneously transmitted in an MCWstructure;

FIG. 15 illustrates precoding matrixes used in one embodiment of ahybrid ARQ scheme for the case where errors occur in some of a pluralityof packets which are simultaneously transmitted in an MCW structure;

FIG. 16 illustrates precoding matrixes used in one embodiment of anantenna hopping ARQ scheme for the case where errors occur in some of aplurality of packets which are simultaneously transmitted in an MCWstructure;

FIG. 17 illustrates precoding matrixes used in another embodiment of aphase shift diversity ARQ scheme for the case where errors occur in someof a plurality of packets which are simultaneously transmitted in an MCWstructure;

FIG. 18 is a block diagram illustrating a transmitting/receivingapparatus which supports a hybrid ARQ scheme based on a multiple antennasystem according to the present invention;

FIG. 19 is a block diagram illustrating an SCW OFDM transmitterconstituting a wireless communication module of FIG. 18;

FIG. 20 is a block diagram illustrating an MCW OFDM transmitterconstituting a wireless communication module of FIG. 18;

FIG. 21A and FIG. 21B illustrate a concept of a phase shift basedprecoding scheme in which a sub-carrier index offset is fed back inaccordance with the present invention;

FIG. 22A and FIG. 22B illustrate a concept of a phase shift basedprecoding scheme in which a phase value offset is fed back in accordancewith the present invention; and

FIG. 23A and FIG. 23B illustrate a concept of a phase shift basedprecoding scheme in which a sub-carrier index offset and a phase valueoffset are fed back in accordance with the present invention.

BEST MODE FOR CARRYING OUT THE INVENTION

Reference will now be made in detail to the preferred embodiments of thepresent invention, examples of which are illustrated in the accompanyingdrawings.

The present invention relates to a method for correcting errors in amultiple antenna system and a transmitting/receiving apparatussupporting the same, which can be applied to a frequency selectivechannel whose change is frequent in addition to a flat fading channel,can be applied to both a single codeword structure and a multi codewordstructure, and to which adaptive ARQ can be applied. To this end, in thepresent invention, a phase shift based precoding scheme is used, whichcan reconstruct or change a precoding matrix depending a spatialmultiplexing rate and various kinds of offset information, and if NACKsignal is arrived from a receiver due to transmission errors, there aresuggested a first method of performing retransmission afterreconstructing a precoding matrix to reduce the spatial multiplexingrate and a second method of performing retransmission after changing aprecoding matrix by using predetermined offset information fed back froma receiver.

<First Embodiment>

As described above, cyclic delay diversity or phase shift diversity isadvantageous in that it can be applied to both an open loop system and aclosed loop system depending on a cyclic delay value and can simply beimplemented. However, a problem occurs in that a data transmission rateis reduced due to a spatial multiplexing rate of 1. Also, althoughcodebook based precoding is advantageous in that efficient datatransmission can be performed by feedback of index, problems occur inthat the codebook based precoding is not suitable for a mobileenvironment in which channel change is frequent and that memory useincreases as a codebook should be provided at both sides of atransmitter/receiver. Accordingly, the present invention suggests aphase shift based precoding method, which can easily change precodingmatrixes depending on circumstances and has advantages of phase shiftdiversity and precoding, and a method for correcting errors, whichincludes ARQ scheme.

Hereinafter, the phase shift based precoding method and the ARQ schemeof the first method based on the phase shift based precoding method willbe described. Subsequently, a transmitting/receiving apparatus whichsupports the ARQ scheme of the first method will be described.

Phase Shift Based Precoding Method

A phase shift based precoding matrix P suggested in the presentinvention may be generalized and expressed as follows.

$\begin{matrix}{P_{N_{t} \times R}^{k} = \begin{pmatrix}w_{1,1}^{k} & w_{1,2}^{k} & \ldots & w_{1,R}^{k} \\w_{2,1}^{k} & w_{2,2}^{k} & \ldots & w_{2,R}^{k} \\\vdots & \vdots & \ddots & \vdots \\w_{N_{t},1}^{k} & w_{N_{t},2}^{k} & \ldots & w_{N_{t},R}^{k}\end{pmatrix}} & \left\lbrack {{Equation}\mspace{14mu} 1} \right\rbrack\end{matrix}$

where, w_(ij) ^(k) (i=1, . . . , N_(t), j=1, . . . , R) denotes acomplex weighted value determined by a sub-carrier index k, N_(t)denotes the number of transmitting antennas or virtual antennas (valueequal to a spatial multiplexing rate, N_(t)=R), and R denotes a spatialmultiplexing rate. The complex weighted value may vary depending on OFDMsymbols which are multiplied by the antennas and the index of thecorresponding sub-carrier.

Meanwhile, the precoding matrix P of Equation 1 is preferably designedby a unitary matrix in order to reduce the loss of channel capacity in amultiple antenna system. In order to check a condition for configuringthe unitary matrix, the channel capacity of the multiple antenna systemis expressed by Equation 2.

$\begin{matrix}{{{Cu}(H)} = {\log_{2}\left( {\det\left( {I_{Nr} + {\frac{SNR}{N}{HH}^{H}}} \right)} \right)}} & \left\lbrack {{Equation}\mspace{14mu} 2} \right\rbrack\end{matrix}$

where, H denotes an N_(r)×N_(t) sized multiple antenna channel matrixand N_(r) denotes the number of receiving antennas. Equation 3 isobtained by applying the phase shift based precoding matrix P toEquation 2.

$\begin{matrix}{C_{precoding} = {\log_{2}\left( {\det\left( {I_{N_{r}} + {\frac{SNR}{N}{HPP}^{H}H^{H}}} \right)} \right)}} & \left\lbrack {{Equation}\mspace{14mu} 3} \right\rbrack\end{matrix}$

As can be seen from Equation 3, in order to eliminate the loss of thechannel capacity, PP^(H) should become an identity matrix. Accordingly,the phase shift based precoding matrix P should satisfy Equation 4.PP ^(H) =I _(N)  [Equation 4]

In order to allow the phase shift based precoding matrix P to become theunitary matrix, two types of conditions, that is, a power constraintcondition and an orthogonality constraint condition, should be satisfiedsimultaneously. The power constraint condition allows the level of eachcolumn of the matrix to become 1, and the orthogonality constraintcondition allows the respective columns of the matrix to have orthogonalcharacteristics. These are respectively expressed by Equations 5 and 6.

$\begin{matrix}{{{{{w_{1,1}^{k}}^{2} + {w_{2,1}^{k}}^{2} + \ldots + {w_{N_{t},1}^{k}}^{2}} = 1},{{{w_{1,2}^{k}}^{2} + {w_{2,2}^{k}}^{2} + \ldots + {w_{N_{t},2}^{k}}^{2}} = 1},\vdots}{{{w_{1,R}^{k}}^{2} + {w_{2,R}^{k}}^{2} + \ldots + {w_{N_{t},R}^{k}}^{2}} = 1}} & \left\lbrack {{Equation}\mspace{14mu} 5} \right\rbrack \\{{{{{w_{1,1}^{k*}w_{1,2}^{k}} + {w_{2,1}^{k*}w_{2,2}^{k}} + \ldots + {w_{N,1}^{k*}w_{N,1}^{k}}} = 0},{{{w_{1,1}^{k*}w_{1,3}^{k}} + {w_{2,1}^{k*}w_{2,3}^{k}} + \ldots + {w_{N,1}^{k*}w_{N,3}^{k}}} = 0},\vdots}{{{w_{1,1}^{k*}w_{1,R}^{k}} + {w_{2,1}^{k*}w_{2,R}^{k}} + \ldots + {w_{N,1}^{k*}w_{N,R}^{k}}} = 0}} & \left\lbrack {{Equation}\mspace{14mu} 6} \right\rbrack\end{matrix}$

Next, an example of the generalized equation of a 2×2 phase shift basedprecoding matrix is provided, and equations for satisfying the twoconstraint conditions are obtained as follows. Equation 7 shows ageneralized equation of a phase shift based precoding matrix when thenumber of transmitting antennas is 2 and a spatial multiplexing rate is2.

$\begin{matrix}{P_{2 \times 2}^{k} = \begin{pmatrix}{\alpha_{1}{\mathbb{e}}^{j\; k\;\theta_{1}}} & {\beta_{1}{\mathbb{e}}^{j\; k\;\theta_{2}}} \\{\beta_{2}{\mathbb{e}}^{j\; k\;\theta_{3}}} & {\alpha_{2}{\mathbb{e}}^{j\; k\;\theta_{4}}}\end{pmatrix}} & \left\lbrack {{Equation}\mspace{14mu} 7} \right\rbrack\end{matrix}$

where, α_(i) and β_(i) (i=1, 2) are real numbers, θ_(i) (i=1, 2, 3, 4)denotes a phase value, and k denotes a sub-carrier index of an OFDMsignal. In order to implement the precoding matrix with the unitarymatrix, the power constraint condition of Equation 8 and theorthogonality constraint condition of Equation 9 should be satisfied.|α₁ e ^(jkθ) ¹ |²+|β₂ e ^(jkθ) ³ |²=1,|α₂ e ^(jkθ) ⁴ |²+|β₁ e ^(jkθ) ²|²=1  [Equation 8](α₁ e ^(jkθ) ¹ )*β₁ e ^(jkθ) ² +(β₂ e ^(jkθ) ³ )*α₂ e ^(jkθ) ⁴=0  [Equation 9]

where, a mark * denotes a conjugate complex number. An example of a 2×2phase shift based precoding matrix which satisfies Equations 7 to 9 isas follows.

$\begin{matrix}{P_{2 \times 2}^{k} = {\frac{1}{\sqrt{2}}\begin{pmatrix}1 & {\mathbb{e}}^{j\; k\;\theta_{2}} \\{\mathbb{e}}^{j\; k\;\theta_{3}} & 1\end{pmatrix}}} & \left\lbrack {{Equation}\mspace{14mu} 10} \right\rbrack\end{matrix}$

where, θ₂ and θ₃ have a relationship expressed by Equation 11 accordingto the orthogonality constraint.kθ ₃ =−kθ ₂+π  [Equation 11]

The precoding matrix may be stored in the memories of the transmitterand the receiver in a codebook form, and the codebook may include avariety of precoding matrixes generated using different finite valuesθ₂. The values θ₂ may properly be set depending on the channel statusand the presence of the feedback information. If the feedbackinformation is used, the values θ₂ are set to small values, and, if thefeedback information is not used, the values θ₂ are set to large values,whereby a high frequency diversity gain can be obtained.

Meanwhile, the spatial multiplexing rate may be set to be smaller thanthe number of antennas depending on the channel status even though thephase shift based precoding matrix is generated as shown in Equation 7.In this case, the generated phase shift based precoding matrix may newlybe reconstructed by selecting a number of specific columns correspondingto the current spatial multiplexing rate (reduced spatial multiplexingrate) from the generated phase shift based precoding matrix. In otherwords, a new precoding matrix applied to a corresponding system is notgenerated whenever the spatial multiplexing rate varies but the originalphase shift based precoding matrix is used as it is, wherein a specificcolumn of the corresponding precoding matrix is selected to reconstructthe precoding matrix.

For example, the precoding matrix of Equation 10 sets the spatialmultiplexing rate of 2 in a multiple antenna system having twotransmitting antennas. However, the spatial multiplexing rate may belowered to 1 for some reason. In this case, a specific column of thematrix shown in Equation 10 may be selected to perform precoding. If thesecond column is selected, the phase shift based precoding matrix isequal to Equation 12 below, which becomes the same format as the cyclicdelay diversity scheme of two transmitting antennas according to therelated art.

$\begin{matrix}{P_{2 \times 1}^{k} = {\frac{1}{\sqrt{2}}\begin{pmatrix}{\mathbb{e}}^{j\; k\;\theta_{2}} \\1\end{pmatrix}}} & \left\lbrack {{Equation}\mspace{14mu} 12} \right\rbrack\end{matrix}$

Although the example of the system having two transmitting antennas hasbeen described, application of the present invention can be expanded toa system having four transmitting antennas. In other words, after thephase shift based precoding matrix is generated in the system havingfour transmitting antennas, a specific column may be selected dependingon the variable spatial multiplexing rate to perform precoding. Forexample, FIG. 9 illustrates that the related art spatial multiplexingand cyclic delay diversity are applied to a multiple antenna systemhaving four transmitting antennas and a spatial multiplexing rate of 2,and FIG. 10 illustrates that the phase shift based precoding matrix ofEquation 10 is applied to the above multiple antenna system.

Referring to FIG. 9, a first sequence S₁ and a second sequence S₂ aretransferred to a first antenna and a third antenna, and the firstsequence s₁e^(jθ) ¹ and the second sequence s₂e^(jθ) ¹ which arephase-shifted at a predetermined level are transferred to a secondantenna and a fourth antenna. Accordingly, it is noted that the spatialmultiplexing rate becomes 2.

By contrast, referring to FIG. 10, s₁+s₂e^(jkθ) ² is transferred to thefirst antenna, s₁e^(jkθ) ³ +s₂ to the second antenna, s₁e^(jkθ) ¹+s₂e^(jk(θ) ¹ ^(+θ) ² ⁾ to the third antenna, and s₁e^(jk(θ) ¹ ^(+θ) ³⁾+s₂e^(jkθ) ¹ to the fourth antenna. Accordingly, since the system ofFIG. 10 has an advantage of the cyclic delay diversity scheme along withan advantage of the precoding scheme as cyclic delay (or phase shift) isperformed for four antennas by using a single precoding matrix.

The aforementioned phase shift based precoding matrix for each spatialmultiplexing rate for the two-antenna system and the four-antenna systemis expressed as follows.

TABLE 2 Two-antenna system Four-antenna system Spatial multiplexingSpatial multiplexing Spatial multiplexing Spatial multiplexing rate of 1rate of 2 rate of 1 rate of 2 $\frac{1}{\sqrt{2}}\begin{pmatrix}1 \\e^{j\;\theta_{1}^{k}}\end{pmatrix}$ $\frac{1}{\sqrt{2}}\begin{pmatrix}1 & {- e^{{- j}\;\theta_{1}^{k}}} \\e^{j\;\theta_{1}^{k}} & 1\end{pmatrix}$ $\frac{1}{\sqrt{4}}\begin{pmatrix}1 \\e^{j\;\theta_{1}^{k}} \\e^{j\;\theta_{2}^{k}} \\e^{j\;\theta_{3}^{k}}\end{pmatrix}$ $\frac{1}{\sqrt{4}}\begin{pmatrix}1 & {- e^{{- j}\;\theta_{1}^{k}}} \\e^{j\;\theta_{1}^{k}} & 1 \\e^{j\;\theta_{2}^{k}} & {- e^{{- j}\;\theta_{3}^{k}}} \\e^{j\;\theta_{3}^{k}} & e^{{- j}\;\theta_{2}^{k}}\end{pmatrix}$

In Table 2, θ_(i)(i=1, 2, 3) denotes a phase angle according to a cyclicdelay value, and K is a sub-carrier index of OFDM. In Table 2, each ofthe four types of the precoding matrixes can be obtained by a specificpart of a precoding matrix for the multiple antenna system having fourtransmitting antennas and a spatial multiplexing rate of 2 as shown inFIG. 11. Accordingly, since the codebook does not need each precodingmatrix for the four types, memory capacity of the transmitter and thereceiver can be saved. The aforementioned phase shift based precodingmatrix can be expanded to a system having M number of antennas (M is anatural number greater than 2) and a spatial multiplexing rate of N (Nis a natural number greater than 1) by the same principle.

Although the procedure of configuring the phase shift based precodingmatrix having four transmitting antennas and the spatial multiplexingrate of 2 has been described as above, the phase shift based precodingmay be generalized by Equation 13 below for a system having N_(t) numberof antennas (N_(t) is a natural number greater than 2) and a spatialmultiplexing rate of R (R is a natural number greater than 1).Hereinafter, the generalized phase shift based precoding will bereferred to as generalized phase shift diversity (GPSD).

$\begin{matrix}{P_{N_{t} \times R}^{k} = {\begin{pmatrix}{\mathbb{e}}^{j\;\theta_{1}k} & 0 & \ldots & 0 \\0 & {\mathbb{e}}^{j\;\theta_{2}k} & \ldots & 0 \\\vdots & \vdots & \ddots & 0 \\0 & 0 & \ldots & {\mathbb{e}}^{j\;\theta\; N_{t}k}\end{pmatrix}U_{N_{t} \times R}}} & \left\lbrack {{Equation}\mspace{14mu} 13} \right\rbrack\end{matrix}$

where, P_(N) _(t) ^(k)×R denotes a GPSD matrix for the kth sub-carrierof a MIMO-OFDM signal having N_(t) number of transmitting antennas and aspatial multiplexing rate of R, and U_(N) _(t) _(×R) is a unitary matrix(second matrix) which satisfies U_(N) _(t) _(×R) ^(H)×U_(N) _(t)_(×R)=II_(R×R) and is used to allow a phase shift matrix (first matrix)to become a unitary matrix. In Equation 13, a phase angle θ_(i)(t), i=1,. . . , N_(t) can be obtained as follows in accordance with a delayvalue of τ_(i)(t), i=1, . . . , N_(t).θ_(i)=−2π/N _(fft)·τ_(i)  [Equation 14]

where, N_(fft) denotes the number of sub-carriers of an OFDM signal.

An example of a generation equation of a GPSD matrix is as follows whenthe number of transmitting antennas is 2 and a 1-bit codebook is used.

In Equation 15, since a value β is easily determined if a value α isdetermined, information of the value α is obtained in such a manner thattwo types of values α are determined and their information is fed backby a codebook index. For example, the value α is previously determinedbetween the transmitter and the receiver that α is equal to 0.2 if afeedback index is 0 while α is equal to 0.8 if a feedback index is 1.

A predetermined precoding matrix for obtaining SNR gain can be used asan example of the second matrix. When Walsh code is used as theprecoding matrix, a generation equation of the phase shift basedprecoding matrix P is as follow.

$\begin{matrix}{P_{4 \times 4}^{k} = {\frac{1}{\sqrt{4}}\begin{pmatrix}{\mathbb{e}}^{j\;\theta_{1}k} & 0 & 0 & 0 \\0 & {\mathbb{e}}^{j\;\theta_{2}k} & 0 & 0 \\0 & 0 & {\mathbb{e}}^{j\;\theta_{3}k} & 0 \\0 & 0 & 0 & {\mathbb{e}}^{j\;\theta_{4}k}\end{pmatrix}\begin{pmatrix}1 & 1 & 1 & 1 \\1 & {- 1} & 1 & {- 1} \\1 & 1 & {- 1} & {- 1} \\1 & {- 1} & {- 1} & 1\end{pmatrix}}} & \left\lbrack {{Equation}\mspace{14mu} 16} \right\rbrack\end{matrix}$

Equation 16 is based on a system having four transmitting antennas and aspatial multiplexing rate of 4. In this case, the second matrix isproperly reconstructed to select a specific transmitting antenna or tunethe spatial multiplexing rate.

Equation 17 shows that the second matrix is reconstructed to select twoantennas in a system having four transmitting antennas.

$\begin{matrix}{P_{4 \times 4}^{k} = {\frac{1}{\sqrt{4}}\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{1}k} & 0 & 0 & 0 \\0 & {\mathbb{e}}^{{j\theta}_{2}k} & 0 & 0 \\0 & 0 & {\mathbb{e}}^{{j\theta}_{3}k} & 0 \\0 & 0 & 0 & {\mathbb{e}}^{{j\theta}_{4}k}\end{pmatrix}\begin{pmatrix}0 & 0 & 1 & 1 \\0 & 0 & 1 & {- 1} \\1 & 1 & 0 & 0 \\1 & {- 1} & 0 & 0\end{pmatrix}}} & \left\lbrack {{Equation}\mspace{14mu} 17} \right\rbrack\end{matrix}$

Also, Table 3 shows a method for reconstructing the second matrixsuitable for a spatial multiplexing rate when the spatial multiplexingrate varies depending on time or channel status.

Although Equation 18 shows that first column, first and second columns,and first to fourth columns of the second matrix are selected dependingon the multiplexing rate, any one of first, second, third and fourthcolumns may be selected if the multiplexing rate is 1 while any two ofthe first, second, third and fourth columns may be selected if themultiplexing rate is 2.

Meanwhile, the second matrix may be provided in the transmitter and thereceiver in the codebook form. In this case, index information of thecodebook is fed back from the receiver to the transmitter, and thetransmitter selects a unitary matrix (latter half matrix) of thecorresponding index from its codebook and then constructs a phase shiftbased precoding matrix by using Equation 13 above.

Furthermore, the second matrix may be changed periodically so thatcarriers transmitted to one time slot have different precoding matrixesfor each frequency band.

Meanwhile, a cyclic delay value for the phase shift based precodingcould be a value previously determined in the transmitter and thereceiver or a value transmitted from the receiver to the transmitterthrough feedback. Also, although the spatial multiplexing rate R may bea value previously determined in the transmitter and the receiver, thereceiver may calculate the spatial multiplexing rate by checking thechannel status and feed back the calculated value to the transmitter.Alternatively, the transmitter may calculate and change the spatialmultiplexing rate by using channel information fed back from thereceiver.

The expanded type of the aforementioned phase shift based precoding canbe expressed as follows.

$\begin{matrix}{P_{N_{t} \times R}^{k} = {\underset{\underset{D_{1}}{︸}}{\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{1}k} & 0 & \ldots & 0 \\0 & {\mathbb{e}}^{{j\theta}_{2}k} & \ldots & 0 \\\vdots & \vdots & \ddots & 0 \\0 & 0 & 0 & {\mathbb{e}}^{{j\theta}_{4}k}\end{pmatrix}}\left( W_{N_{t} \times R} \right)\underset{\underset{D_{2}}{︸}}{\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{1}^{\prime}k} & 0 & \ldots & 0 \\0 & {\mathbb{e}}^{{j\theta}_{2}^{\prime}k} & \ldots & 0 \\\vdots & \vdots & \ddots & 0 \\0 & 0 & 0 & {\mathbb{e}}^{{j\theta}_{R}^{\prime}k}\end{pmatrix}}\left( U_{R \times R} \right)}} & \left\lbrack {{Equation}\mspace{14mu} 19} \right\rbrack\end{matrix}$

In Equation 19 above, D₁ is used to change a channel, and D₂ is used toequalize a channel between respective streams. Also, W_(N) _(t) _(×R)and U_(R×R) denote unitary matrixes.

Now, a procedure of performing ARQ for error correction using theaforementioned phase shift based precoding will be described. It isassumed that initial transmission is performed using a precoding matrixhaving two transmitting antennas and a spatial multiplexing rate of 2 ina multiple codeword (MCW) structure. However, as described above, aprecoding matrix for a system having M number of antennas (M is anatural number greater than 2) and a spatial multiplexing rate of N (Nis a natural number greater than 1) may be used, and a single codeword(SCW) structure may be used.

In the multiple codeword structure, a plurality of packets may betransmitted simultaneously through spatial multiplexing. Packettransmission can be performed by two types of cases. That is, the formercase corresponds to the case where errors occur in all packets eventhough i number of packets (i is a natural number greater than 2) havebeen transmitted, and the latter case corresponds to the case whereerrors occur in j number of packets (j is a natural number smaller thani) even though i number of packets have been transmitted. First of all,the former case will be described.

As shown in FIG. 12, a precoding matrix having a spatial multiplexingrate of 2 is used during initial transmission, and if NACK signal isarrived from the receiver due to transmission packet errors, theprecoding matrix is reconstructed such that the first column or thesecond column is selected from the precoding matrix during initialtransmission to obtain the spatial multiplexing rate of 1. Then, ARQ isperformed. If the spatial multiplexing rate is lowered, the transmissionpower can be increased, whereby transmission reliability can beimproved. At this time, transmitting antennas used for retransmissioncan be selected as those having excellent channel status referring tochannel quality information transmitted from the receiver.

Next, if errors occur in some of the transmitted packets like the lattercase, two types of ARQ schemes can be considered. In case of the firsttype, only packets in which errors occur are retransmitted, and aspatial resource for normal packets is not used for retransmission. Thistype is called a blanking method. According to the blanking method, anew packet is not transmitted until j number of packets in which errorsoccur are restored by ARQ. In case of the second type, j number ofpackets are retransmitted and at the same time a new packet istransmitted through a spatial resource for the other packets. This typeis called a non-blanking method.

-   -   Multiple Antenna Based ARQ Scheme in Blanking Method

1. Antenna Hopping ARQ Scheme

Antennas other than transmitting antennas used for initial transmissionare selected for retransmission.

2. Antenna Selection ARQ Scheme

Transmitting antennas for retransmission are selected throughtransmitting antenna related information fed back from the receiver.Alternatively, transmitting antennas are randomly selected throughdirect channel estimation at the transmitter to perform retransmission.

3. Phase Shift Diversity ARQ Scheme

The spatial multiplexing scheme or the phase shift diversity scheme isused during initial transmission, and a phase shift based precodingmethod having a spatial multiplexing rate corresponding to the number ofpackets in which errors occur is used during retransmission.

In other words, as shown in FIG. 13, the spatial multiplexing schemehaving a spatial multiplexing rate of 2 is used during initialtransmission. If errors occur in the transmission packets,retransmission is performed in such a manner that the first column orthe second column is selected from the phase shift based precodingmatrix of the two-transmitting antenna system to reconstruct theprecoding matrix having a spatial multiplexing rate of 1. Also, as shownin FIG. 14, the phase shift diversity scheme having a spatialmultiplexing rate of 2 is used during initial transmission. If errorsoccur in the transmission packets, retransmission is performed in such amanner that the first column or the second column is selected from thephase shift based precoding matrix of the two-transmitting antennasystem to reconstruct the precoding matrix having a spatial multiplexingrate of 1. Alternatively, retransmission is performed by changingtransmitting antennas even though the phase shift based precoding matrixis used.

4. Hybrid ARQ Scheme

If errors occur in j number of packets, the antenna hopping ARQ schemeor the phase shift diversity ARQ scheme is used. If errors occur in allpackets, the time-space symbol based HARQ of FIG. 8 is used. FIG. 15illustrates the procedure of performing the phase shift diversity ARQscheme when errors occur in some packets and performing the time-spacesymbol based HARQ when errors occur in all packets.

-   -   Multiple Antenna Based ARQ Scheme in Non-Blanking Method

1. Antenna Hopping ARQ Scheme

Antennas other than transmitting antennas used for initial transmissionare selected to perform retransmission. FIG. 16 illustrates theprocedure of hopping antennas for retransmission when packets aretransmitted through the phase shift diversity scheme.

2. Phase Shift Diversity ARQ Scheme

The spatial multiplexing scheme or the phase shift diversity scheme isused for initial transmission. The phase shift based precoding method isused for retransmission, wherein the position of each column in theprecoding matrix is varied. FIG. 17 illustrates the procedure ofexchanging respective columns of the phase shift based precoding matrixduring retransmission when packets are transmitted through the phaseshift diversity scheme.

3. Hybrid ARQ Scheme

If errors occur in j number of packets, the antenna hopping ARQ schemeor the phase shift diversity ARQ scheme in the non-blanking method isused. If errors occur in all packets, the time-space symbol based HARQof FIG. 8 is used.

At least any one of channel-adaptive HARQ/channel-non-adaptive HARQ,chase combining scheme/incremental redundancy scheme, and synchronousHARQ/asynchronous HARQ may be used as the aforementioned ARQ scheme.

Transmitting and Receiving Apparatus which Supports First Method

FIG. 18 is a block diagram illustrating internal configuration of atransmitting and receiving apparatus which supports the first method.The transmitting and receiving apparatus includes an input module 1801selecting a desired function or inputting information, a display module1803 displaying various kinds of information for operating thetransmitting and receiving apparatus, a memory module 1805 storingvarious programs required for the operation of the transmitting andreceiving apparatus and data to be transmitted to the receiver, awireless communication module 1807 receiving an external signal andtransmitting data to the receiver, an audio processor 1809 converting adigital audio signal into an analog audio signal, amplifying the signaland outputting the amplified signal through a speaker SP or amplifyingthe audio signal from a mike MIC and converting the signal into adigital signal, and a controller 1811 controlling entire driving of thetransmitting and receiving apparatus.

The configuration of the wireless communication module 1807 will bedescribed in more detail. FIG. 19 illustrates the configuration of asingle codeword (SCW) OFDM transmitter included in the wirelesscommunication module 1807, and FIG. 20 illustrates the configuration ofan MCW OFDM transmitter included in the wireless communication module1807. Also, since the receiver corresponding to the transmitter includesmodules having inverse functions of the respective modules of thetransmitter, its detailed description will be omitted.

In the SCW OFDM transmitter, a channel encoder 1910 adds redundant bitsto transmission data bits to prevent the transmission bits from beingdistorted in a channel, and performs channel encoding by using anencoding code such as LDPC code. An interleaver 1920 performsinterleaving through code bit parsing to minimize loss due toinstantaneous noise in data transmission, and a mapper 1930 converts theinterleaved data bits into OFDM symbols. This symbol mapping can beperformed through phase modulation such as QPSK or amplitude modulationsuch as 16QAM, 8QAM and 4QAM. Afterwards, the OFDM symbols are carriedin carriers of a time domain through a precoder 1940, a subchannelmodulator (not shown), and an IFFT 1950, sequentially, and thentransmitted to a radio channel through a filter (not shown) and ananalog converter 1960. Meanwhile, the MCW OFDM transmitter has the sameconfiguration as that of the SCW OFDM transmitter excluding that OFDMsymbols are arranged in parallel for each channel and then transmittedto a channel encoder 2010 and an interleaver 2020.

Precoding matrix determination modules 1941 and 2041 determine the firstprecoding matrix for sub-carriers of the first index, and phase shiftsthe first precoding matrix to determine precoding matrixes for the othersub-carriers. In the present invention, precoding is performed using aunitary matrix of (the number of transmitting antennas)×(spatialmultiplexing rate) size, wherein the unitary matrix is provided for eachindex of sub-carriers. The unitary matrix for the first index is phaseshifted to obtain unitary matrixes of the other indexes. This will bedescribed in more detail.

In other words, the precoding matrix determination modules 1941 and 2041select a random precoding matrix in a codebook previously stored in amemory (not shown) and determines the selected precoding matrix as aprecoding matrix (first precoding matrix) for sub-carrier of the firstindex. In this case, the first precoding matrix may also be selecteddepending on predetermined policies, channel status, etc.

Subsequently, the first precoding matrix is phase shifted at apredetermined size to generate a second precoding matrix for sub-carrierof the second index. At this time, the size of the shifted phase may beset depending on the current channel status and/or the presence offeedback information from the receiver. The second precoding matrix isphase shifted at a predetermined size to generate a third precodingmatrix for sub-carrier of the third index. In other words, the procedureof generating the second precoding matrix is repeated in the procedureof generating the third precoding matrix to the last precoding matrix.

Precoding matrix reconstruction modules 1942 and 2042 are previously setin the memory from each precoding matrix generated in the precodingmatrix generation modules 1941 and 2041 or reconstruct the precodingmatrixes depending on information reported from a controller 1811. Inthis case, reconstruction of the precoding matrixes may vary dependingon types of ARQ schemes supported by the transmitting and receivingapparatus. In other words, reconstruction of the precoding matrixes maybe performed in such a manner that a specific column of the precodingmatrix is selected to lower the spatial multiplexing rate or theposition of each row or column of the precoding matrix is exchanged.

Precoding modules 1943 and 2043 perform precoding by substituting OFDMsequence of the corresponding sub-carrier for the reconstructedprecoding matrix.

In addition, if the transmitting and receiving apparatus supports anyone of the antenna hopping ARQ scheme, the antenna selection ARQ scheme,the phase shift diversity ARQ scheme, and the hybrid ARQ scheme in theblanking method or any one of the antenna hopping ARQ scheme, the phaseshift diversity ARQ scheme, and the hybrid ARQ scheme in thenon-blanking method, the transmitting and receiving apparatus mayfurther include any one or more of a spatial multiplexing module (notshown), a phase shift diversity module (not shown), and a time-spacesymbol module (not shown).

The controller 1811 reports various kinds of information for changing orreconstructing the precoding matrix depending on the ARQ schemesupported by the transmitting and receiving apparatus to the precodingmatrix reconstruction modules 1942 and 2042 or updates spatialmultiplexing rate information stored in the memory so that the precodingmatrix reconstruction modules 1942 and 2042 are operated referring tothe updated information.

<Second Embodiment>

In the aforementioned first method, a corresponding precoding matrix ischanged such that phase value offset and/or sub-carrier index offsetinformation, which is fed back from the receiver or randomly set in thetransmitter, is applied to the phase shift based precoding matrix beforereconstruction to lower the spatial multiplexing rate, whereby aprecoding matrix optimized for retransmission can be obtained.Hereinafter, the procedure of changing the precoding matrix by allowingthe system having four antennas and a spatial multiplexing rate of 2 toapply phase value offset and/or sub-carrier index offset to the phaseshift based precoding matrix in Table 2 will be described in accordancewith embodiments. In this case, it will be apparent to those withordinary skill in the art to which the present invention pertains thatthe improved phase shift based precoding method of the present inventionis not limited to the following embodiments and is applicable to asystem having M number of antennas (M is a natural number greater than2) and a spatial multiplexing rate of N (N is a natural number greaterthan 1).

<First Feedback Embodiment>

In this embodiment, as shown in FIG. 21A, sub-carrier index offsetN_(offset) is fed back from the receiver and then applied to the phaseshift based precoding matrix.

As shown in FIG. 21B, it is noted that a channel area (area allocatedfor a solid line sine wave) initially allocated to sub-carrier of indexk is relatively poorer than the other areas. Accordingly, the receiverchecks the channel status of the resource allocated to the correspondingsub-carrier, sets a proper offset N_(offset), and feeds back the setoffset N_(offset) to the transmitter. The transmitter applies thefed-back offset N_(offset) to the existing phase shift based precodingmatrix so that the corresponding sub-carrier moves to the optimizedchannel area (area allocated for a dotted line sine wave). An equationof the phase shift based precoding matrix to which the fed-back indexoffset N_(offset) has been applied can be expressed as follows.

$\begin{matrix}{\frac{1}{\sqrt{4}}\begin{pmatrix}1 & {- {\mathbb{e}}^{- {{j\theta}_{1}{({k + N_{offset}})}}}} \\{\mathbb{e}}^{{j\theta}_{1}{({k + N_{offset}})}} & 1 \\{\mathbb{e}}^{{j\theta}_{2}{({k + N_{offset}})}} & {- {\mathbb{e}}^{- {{j\theta}_{3}{({k + N_{offset}})}}}} \\{\mathbb{e}}^{{j\theta}_{3}{({k + N_{offset}})}} & {\mathbb{e}}^{- {{j\theta}_{2}{({k + N_{offset}})}}}\end{pmatrix}} & \left\lbrack {{Equation}\mspace{14mu} 20} \right\rbrack\end{matrix}$

When Equation 19 is applied to the generalized phase shift diversityscheme, the following Equation 21 can be obtained.

$\begin{matrix}{P_{N_{t} \times R}^{k} = {\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{1}{({k + N_{offset}})}} & 0 & \ldots & 0 \\0 & {\mathbb{e}}^{{j\theta}_{2}{({k + N_{offset}})}} & \ldots & 0 \\\vdots & \vdots & \ddots & 0 \\0 & 0 & \ldots & {\mathbb{e}}^{{j\theta}_{N_{t}}{({k + N_{offset}})}}\end{pmatrix}U_{N_{t} \times R}}} & \left\lbrack {{Equation}\mspace{14mu} 21} \right\rbrack\end{matrix}$

Also, when Equation 19 is applied to the expanded phase shift diversityscheme, the following Equation 22 can be obtained.

$\begin{matrix}{P_{N_{t} \times R}^{k} = {\underset{\underset{D_{1}}{︸}}{\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{1}{({k + N_{offset}})}} & 0 & \ldots & 0 \\0 & {\mathbb{e}}^{{j\theta}_{2}{({k + N_{offset}})}} & \ldots & 0 \\\vdots & \vdots & \ddots & 0 \\0 & 0 & 0 & {\mathbb{e}}^{{j\theta}_{N_{t}}{({k + N_{offset}})}}\end{pmatrix}}W_{N_{t} \times R}\underset{\underset{D_{2}}{︸}}{\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{1}^{\prime}k} & 0 & \ldots & 0 \\0 & {\mathbb{e}}^{{j\theta}_{2}^{\prime}k} & \ldots & 0 \\\vdots & \vdots & \ddots & 0 \\0 & 0 & 0 & {\mathbb{e}}^{{j\theta}_{R}^{\prime}k}\end{pmatrix}}U_{R \times R}}} & \left\lbrack {{Equation}\mspace{14mu} 22} \right\rbrack\end{matrix}$

<Second Feedback Embodiment>

In this embodiment, as shown in FIG. 22A, either a proper phase value θor a phase value offset θ_(offset) which is the difference between aprevious feedback phase value and the optimized phase value is fed backfrom the receiver and then applied to the phase shift based precodingmatrix. Also, a value previously determined depending on the number ofretransmission times may be used as the phase value offset θ_(offset).

As shown in FIG. 22B, it is noted that a channel area (area allocatedfor a solid line sine wave) initially allocated to sub-carrier of indexk having a phase of θ₀ is relatively poorer than the other areas.Accordingly, the receiver checks the channel status of the resourceallocated to the corresponding sub-carrier, sets a proper offset θ,compares the set offset θ with the fed-back phase value θ₀, and feedsback the result offset θ_(offset) which is the difference value to thetransmitter. The transmitter applies the fed-back offset θ_(offset) tothe existing phase shift based precoding matrix so that thecorresponding sub-carrier moves to a channel area (area allocated for adotted line sine wave) which is relatively more excellent than before.An equation of the phase shift based precoding matrix to which thefed-back offset θ_(offset) has been applied can be expressed as follows.

$\begin{matrix}{\frac{1}{\sqrt{4}}\begin{pmatrix}1 & {- {\mathbb{e}}^{{- {j{({\theta_{1} + \theta_{1,{offset}}})}}}k}} \\{\mathbb{e}}^{{j{({\theta_{1} + \theta_{1,{offset}}})}}k} & 1 \\{\mathbb{e}}^{{j{({\theta_{2} + \theta_{2,{offset}}})}}k} & {- {\mathbb{e}}^{{- {j{({\theta_{3} + \theta_{3,{offset}}})}}}k}} \\{\mathbb{e}}^{{j{({\theta_{3} + \theta_{3,{offset}}})}}k} & {\mathbb{e}}^{{- {j{({\theta_{2} + \theta_{2,{offset}}})}}}k}\end{pmatrix}} & \left\lbrack {{Equation}\mspace{14mu} 23} \right\rbrack\end{matrix}$

Meanwhile, if the receiver checks the status of the channel allocated tothe corresponding sub-carrier, sets an optimized phase value θ, anddirectly feeds back the set value to the transmitter, the transmittermay newly generate the phase shift based precoding matrix based on thefed-back phase value.

When Equation 23 is applied to the generalized phase shift diversityscheme, the following Equation 24 can be obtained.

$\begin{matrix}{P_{N_{t} \times R}^{k} = {\begin{pmatrix}{\mathbb{e}}^{{j{({\theta_{1} + \theta_{1,{offset}}})}}k} & 0 & \ldots & 0 \\0 & {\mathbb{e}}^{{j{({\theta_{2} + \theta_{2,{offset}}})}}k} & \ldots & 0 \\\vdots & \vdots & \ddots & 0 \\0 & 0 & \ldots & {\mathbb{e}}^{{j{({\theta_{N_{t}} + \theta_{N_{t},{offset}}})}}k}\end{pmatrix}U_{N_{t} \times R}}} & \left\lbrack {{Equation}\mspace{14mu} 24} \right\rbrack\end{matrix}$

Also, when Equation 23 is applied to the expanded phase shift diversityscheme, the following Equation 25 can be obtained.

$\begin{matrix}{P_{N_{t} \times R}^{k} = {\underset{\underset{D_{1}}{︸}}{\begin{pmatrix}{\mathbb{e}}^{{j{({\theta_{1} + \theta_{1,{offset}}})}}k} & 0 & \ldots & 0 \\0 & {\mathbb{e}}^{{j{({\theta_{2} + \theta_{2,{offset}}})}}k} & \ldots & 0 \\\vdots & \vdots & \ddots & 0 \\0 & 0 & \ldots & {\mathbb{e}}^{{j{({\theta_{N_{t}} + \theta_{N_{t},{offset}}})}}k}\end{pmatrix}}W_{N_{t} \times R}\underset{\underset{D_{2}}{︸}}{\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{1}^{\prime}k} & 0 & \ldots & 0 \\0 & {\mathbb{e}}^{{j\theta}_{2}^{\prime}k} & \ldots & 0 \\\vdots & \vdots & \ddots & 0 \\0 & 0 & 0 & {\mathbb{e}}^{{j\theta}_{R}^{\prime}k}\end{pmatrix}}U_{R \times R}}} & \left\lbrack {{Equation}\mspace{14mu} 25} \right\rbrack\end{matrix}$

The offset θ_(offset) of Equations 24 and 25 may be fed back from thereceiver. Alternatively, a previously determined value may be used asthe offset θ_(offset) depending on the number of retransmission times.

<Third Feedback Embodiment>

In this embodiment, as shown in FIG. 23A, a proper phase value θ and asub-carrier index offset are fed back from the receiver. Alternatively,a phase value offset θ_(offset) which is the difference between theprevious feedback phase value and the optimized phase value and asubcarier index offset N_(offset) are fed back from the receiver. Thus,the resultant values are applied to the phase shift based precodingmatrix.

As shown in FIG. 23B, it is noted that a channel area (area allocatedfor a solid line sine wave) initially allocated to sub-carrier of indexk having a phase of θ₀ is relatively poorer than the other areas.Accordingly, the receiver checks the channel status of the resourceallocated to the corresponding sub-carrier, sets a phase value θ for anoptimized status and a sub-carrier index offset N_(offset), feeds backan offset value θ_(offset) which is the difference between the phasevalue θ and the previous feedback phase value θ₀ and the sub-carrierindex offset N_(offset) to the transmitter. Then, the transmitter addsthe fed-back offset values θ_(offset) and N_(offset) to the existingphase shift based precoding matrix so that the corresponding sub-carriermoves to the optimized channel area (area allocated for a dotted linesine wave). An equation of the phase shift based precoding matrix towhich the fed-back offset values θ_(offset) and N_(offset) have beenapplied can be expressed as follows.

$\begin{matrix}{\frac{1}{\sqrt{4}}\begin{pmatrix}1 & {- {\mathbb{e}}^{{- {j{({\theta_{1} + \theta_{1,{offset}}})}}}k}} \\{\mathbb{e}}^{{j{({\theta_{1} + \theta_{1,{offset}}})}}k} & 1 \\{\mathbb{e}}^{{j{({\theta_{2} + \theta_{2,{offset}}})}}k} & {- {\mathbb{e}}^{{- {j{({\theta_{3} + \theta_{3,{offset}}})}}}k}} \\{\mathbb{e}}^{{j{({\theta_{3} + \theta_{3,{offset}}})}}k} & {\mathbb{e}}^{{- {j{({\theta_{2} + \theta_{2,{offset}}})}}}k}\end{pmatrix}} & \left\lbrack {{Equation}\mspace{14mu} 26} \right\rbrack\end{matrix}$

When Equation 26 is applied to the generalized phase shift diversityscheme, the following Equation 27 can be obtained.

$\begin{matrix}{P_{N_{t} \times R}^{k} = {\begin{pmatrix}{\mathbb{e}}^{{j{({\theta_{1} + \theta_{1,{offset}}})}}{({k + N_{offset}})}} & 0 & \ldots & 0 \\0 & {\mathbb{e}}^{{j{({\theta_{2} + \theta_{2,{offset}}})}}{({k + N_{offset}})}} & \ldots & 0 \\\vdots & \vdots & \ddots & 0 \\0 & 0 & \ldots & {\mathbb{e}}^{{j{({\theta_{N_{t}} + \theta_{N_{t},{offset}}})}}{({k + N_{offset}})}}\end{pmatrix}U_{N_{t} \times R}}} & \left\lbrack {{Equation}\mspace{14mu} 27} \right\rbrack\end{matrix}$

Also, when Equation 28 is applied to the expanded phase shift diversityscheme, the following Equation 28 can be obtained.

$\begin{matrix}{P_{N_{t} \times R}^{k} = {\underset{\underset{D_{1}}{︸}}{\begin{pmatrix}{\mathbb{e}}^{{j{({\theta_{1} + \theta_{1,{offset}}})}}{({k + N_{offset}})}} & 0 & \ldots & 0 \\0 & {\mathbb{e}}^{{j{({\theta_{2} + \theta_{2,{offset}}})}}{({k + N_{offset}})}} & \ldots & 0 \\\vdots & \vdots & \ddots & 0 \\0 & 0 & \ldots & {\mathbb{e}}^{{j{({\theta_{N_{t}} + \theta_{N_{t},{offset}}})}}{({k + N_{offset}})}}\end{pmatrix}}W_{N_{t} \times R}\underset{\underset{D_{2}}{︸}}{\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{1}^{\prime}k} & 0 & \ldots & 0 \\0 & {\mathbb{e}}^{{j\theta}_{2}^{\prime}k} & \ldots & 0 \\\vdots & \vdots & \ddots & 0 \\0 & 0 & 0 & {\mathbb{e}}^{{j\theta}_{R}^{\prime}k}\end{pmatrix}}U_{R \times R}}} & \left\lbrack {{Equation}\mspace{14mu} 28} \right\rbrack\end{matrix}$

<Fourth Feedback Embodiment>

In this embodiment, a sub-carrier index of the phase shift basedprecoding matrix is used as a sub-carrier index offset N_(offset) fedback from the receiver.

The receiver checks the channel status of the resource allocated to arandom sub-carrier or a predetermined sub-carrier, sets a proper offsetN_(offset), and feeds back the set offset to the transmitter. Then, thetransmitter applies the fed-back offset value N_(offset) to the existingphase shift based precoding matrix for all sub-carriers regardless oftypes of sub-carriers (or index of sub-carriers) so that allsub-carriers move to the optimized channel area (area allocated for adotted line sine wave). In other words, since the frequency domainhaving the greatest channel size is equally applied to all sub-carriers,system performance can be improved. An equation of the phase shift basedprecoding matrix to which the fed-back index offset N_(offset) has beenapplied can be expressed as follows.

$\begin{matrix}{\frac{1}{\sqrt{4}}\begin{pmatrix}1 & {- {\mathbb{e}}^{{- {j\theta}_{1}}N_{offset}}} \\{\mathbb{e}}^{{j\theta}_{1}N_{offset}} & 1 \\{\mathbb{e}}^{{j\theta}_{2}N_{offset}} & {- {\mathbb{e}}^{{- {j\theta}_{3}}N_{offset}}} \\{\mathbb{e}}^{{j\theta}_{3}N_{offset}} & {\mathbb{e}}^{{- {j\theta}_{2}}N_{offset}}\end{pmatrix}} & \left\lbrack {{Equation}\mspace{14mu} 29} \right\rbrack\end{matrix}$

In this case, the sub-carrier index offset N_(offset) is a fixed value,and serves as information for the greatest channel size at the receiver.

When Equation 29 is applied to the generalized phase shift diversityscheme, the following Equation 30 can be obtained.

$\begin{matrix}{P_{N_{t} \times R}^{k} = {\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{1}N_{offset}} & 0 & \ldots & 0 \\0 & {\mathbb{e}}^{{j\theta}_{2}N_{offset}} & \ldots & 0 \\\vdots & \vdots & \ddots & 0 \\0 & 0 & \ldots & {\mathbb{e}}^{{j\theta}_{N_{t}}N_{offset}}\end{pmatrix}U_{N_{t} \times R}}} & \left\lbrack {{Equation}\mspace{14mu} 30} \right\rbrack\end{matrix}$

Also, when Equation 29 is applied to the expanded phase shift diversityscheme, the following Equation 31 can be obtained.

$\begin{matrix}{P_{N_{t} \times R}^{k} = {\underset{\underset{D_{1}}{︸}}{\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{1}N_{offset}} & 0 & \ldots & 0 \\0 & {\mathbb{e}}^{{j\theta}_{2}N_{offset}} & \ldots & 0 \\\vdots & \vdots & \ddots & 0 \\0 & 0 & 0 & {\mathbb{e}}^{{j\theta}_{N_{t}}N_{offset}}\end{pmatrix}}W_{N_{t} \times R}\underset{\underset{D_{2}}{︸}}{\begin{pmatrix}{\mathbb{e}}^{{j\theta}_{1}^{\prime}k} & 0 & \ldots & 0 \\0 & {\mathbb{e}}^{{j\theta}_{2}^{\prime}k} & \ldots & 0 \\\vdots & \vdots & \ddots & 0 \\0 & 0 & 0 & {\mathbb{e}}^{{j\theta}_{R}^{\prime}k}\end{pmatrix}}U_{R \times R}}} & \left\lbrack {{Equation}\mspace{14mu} 31} \right\rbrack\end{matrix}$

In the second method of the present invention, if NACK signal is arrivedfrom the receiver due to errors occurring in transmission packets, theexisting phase shift based precoding matrix is changed to any one amongthe matrixes of the first to fourth feedback embodiments by usingvarious kinds of offset information fed back from the receiver and thenpacket retransmission is performed using the changed precoding matrix.Hereinafter, the main configuration of the transmitting and receivingapparatus which supports the second method will be described.

Transmitting and Receiving Apparatus which Supports Second Method

In this transmitting and receiving apparatus, an input module, a displaymodule, a memory module, a wireless communication module, a speaker SP,a mike MIC, an audio processor, a controller, and a channel encoder, aninterleaver, a mapper, a precoder, a subchannel modulator, an IFFT, afilter, and an analog converter which are included in the wirelesscommunication module, and a precoding matrix determination module and aprecoding module which are included in the precoder are the same asthose of the transmitting and receiving apparatus which supports thefirst method. Accordingly, an offset application module (not shown)provided in the precoder instead of the precoding matrix reconstructionmodule will now be described.

The offset application module applies phase value offset information fedback from the receiver and/or sub-carrier index offset information tothe precoding matrix reconstructed by the precoding matrixreconstruction module to finally complete any one among the matrixes ofthe first to fourth feedback embodiments if the transmitting andreceiving apparatus of the present invention is operated in a closedloop system. If the transmitting and receiving apparatus of the presentinvention is operated in an open loop system, the offset applicationmodule applies phase value offset information and/or sub-carrier indexoffset information, which is randomly given from the transmitter.

Meanwhile, a personal digital assistant (PDA), a cellular phone, apersonal communication service (PCS) phone, a global system for mobile(GSM) phone, a wideband CDMA (WCDMA) phone, or a mobile broadband system(MBS) phone may be used as the transmitting and receiving apparatus ofthe present invention.

According to the present invention, the multiple antenna related schemeis combined with the ARQ related scheme to simultaneously improve speedand reliability in data transmission. Also, the present invention can beapplied to a frequency selective channel, allows error processing of amultiple codeword, and can apply adaptive ARQ without being limited tothe specific multiple antenna transmission method.

It will be apparent to those skilled in the art that the presentinvention can be embodied in other specific forms without departing fromthe spirit and essential characteristics of the invention. Thus, theabove embodiments are to be considered in all respects as illustrativeand not restrictive. The scope of the invention should be determined byreasonable interpretation of the appended claims and all change whichcomes within the equivalent scope of the invention are included in thescope of the invention.

INDUSTRIAL APPLICABILITY

The present invention can be applied to a wire communication system suchas a wireless Internet and a mobile communication system.

What is claimed is:
 1. A method for spatial multiplexing (SM)transmission using multiple antennas in a wireless access system, themethod performed by an apparatus and comprising: performing a firsttransmission using a first precoding matrix for the SM transmission; andperforming a second transmission using a second precoding matrix to havea smaller spatial multiplexing rate than the first transmission, whereinthe second precoding matrix is consist of at least one column of thefirst precoding matrix, and wherein a number of the at least one columncorresponds to the smaller spatial multiplexing rate.
 2. The methodaccording to claim 1, wherein the second precoding matrix is selectedbased on a precoding matrix index received from a receiver.
 3. Themethod according to claim 1, wherein the first transmission is performedusing two codewords, and the second transmission is performed using onecodeword.
 4. The method according to claim 3, wherein the secondtransmission is a retransmission of the first transmission.
 5. Themethod according to claim 1, wherein the first and the secondtransmission are open loop SM transmissions.
 6. An apparatus configuredfor spatial multiplexing (SM) transmission using multiple antennas in awireless access system, the apparatus comprising: the multiple antennas;and a controller for supporting the SM transmission, wherein thecontroller controls: the multiple antennas to perform a firsttransmission using a first precoding matrix for the SM transmission; themultiple antennas to perform a second transmission using a secondprecoding matrix to have a smaller spatial multiplexing rate than thefirst transmission, wherein the second precoding matrix is consist of atleast one column of the first precoding matrix, and wherein a number ofthe at least one column corresponds to the smaller spatial multiplexingrate.
 7. The apparatus according to claim 6, wherein the secondprecoding matrix is selected based on a precoding matrix index receivedfrom a receiver.
 8. The apparatus according to claim 6, wherein thefirst transmission is performed using two codewords, and the secondtransmission is performed using one codeword.
 9. The apparatus accordingto claim 8, wherein the second transmission is a retransmission of thefirst transmission.
 10. The apparatus according to claim 6, wherein thefirst and the second transmission are open loop SM transmissions.